Fast Subspace Fluid Simulation with Temporal-Aware Basis

2025-02-07

AI Summary

Real-time fluid simulation in computer graphics demands high temporal responsiveness, memory efficiency, and user controllability—challenges unmet by conventional methods. Method: We propose a subspace fluid modeling framework based on Dynamic Mode Decomposition (DMD), which learns the temporal evolution operator of fluid states rather than the states themselves, enabling low-dimensional, high-fidelity, invertible, and robust simulation. We introduce the first integration of Optimized DMD (OptDMD) and Control-aware DMD (DMDc) into graphics, supporting real-time force-driven control, time-reversible reconstruction, and noise robustness. Randomized SVD and spatiotemporal modulation further reduce basis function count. Results: Our method outperforms traditional reduced-order models in accuracy and efficiency on complex scenarios—including vortex ring collisions and boundary-driven plumes—while enabling artistic editing, turbulence enhancement, and interactive super-resolution rendering. Memory footprint and computational cost are substantially reduced.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

We present a novel reduced-order fluid simulation technique leveraging Dynamic Mode Decomposition (DMD) to achieve fast, memory-efficient, and user-controllable subspace simulation. We demonstrate that our approach combines the strengths of both spatial reduced order models (ROMs) as well as spectral decompositions. By optimizing for the operator that evolves a system state from one timestep to the next, rather than the system state itself, we gain both the compressive power of spatial ROMs as well as the intuitive physical dynamics of spectral methods. The latter property is of particular interest in graphics applications, where user control of fluid phenomena is of high demand. We demonstrate this in various applications including spatial and temporal modulation tools and fluid upscaling with added turbulence. We adapt DMD for graphics applications by reducing computational overhead, incorporating user-defined force inputs, and optimizing memory usage with randomized SVD. The integration of OptDMD and DMD with Control (DMDc) facilitates noise-robust reconstruction and real-time user interaction. We demonstrate the technique's robustness across diverse simulation scenarios, including artistic editing, time-reversal, and super-resolution. Through experimental validation on challenging scenarios, such as colliding vortex rings and boundary-interacting plumes, our method also exhibits superior performance and fidelity with significantly fewer basis functions compared to existing spatial ROMs. The inherent linearity of the DMD operator enables unique application modes, such as time-reversible fluid simulation. This work establishes another avenue for developing real-time, high-quality fluid simulations, enriching the space of fluid simulation techniques in interactive graphics and animation.

Problem

• Fast fluid simulation optimization
• Memory-efficient subspace techniques
• User-controllable fluid dynamics

Innovation

• Dynamic Mode Decomposition
• memory-efficient subspace simulation
• real-time user interaction